write an eguation in standard form of the that passes through the two points. ( 1,4) ( 5,7) please explain.thanks..
The slope of the line is (7-4)/(5-1)= 0.75
The equation of the line is
(y-4)/(x-1) = slope = 0.75
y = 0.75 x + 3.25
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There are other ways to do it. You could write down the standard form y = mx + b and substitute the two pairs of (x,y) numbers,
4 = m + b
7 = 5m + b
and then solve for m and b.
To find the equation of a line in standard form that passes through two points, we need to follow a few steps.
Step 1: Determine the slope (m) of the line using the given points.
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).
Using the given points (1,4) and (5,7), we can substitute these values into the formula:
m = (7 - 4) / (5 - 1)
m = 3 / 4
So, the slope (m) is 3/4.
Step 2: Use the slope-intercept form of a line (y = mx + b) to find the y-intercept (b).
We can choose any of the two given points (1,4) or (5,7) to substitute into the slope-intercept equation.
Let's use the point (1,4) to solve for b:
4 = (3/4) * 1 + b
4 = 3/4 + b
Multiply every term by 4 to eliminate the fraction:
16 = 3 + 4b
16 - 3 = 4b
13 = 4b
b = 13/4
So, the y-intercept (b) is 13/4.
Step 3: Substitute the slope (m) and y-intercept (b) into the standard form equation (Ax + By = C).
Let's multiply every term by 4 to eliminate the fraction:
4y = 3x + 13
To convert this equation into standard form, move all terms to the left side:
3x - 4y = -13
So, the equation in standard form that passes through the points (1,4) and (5,7) is 3x - 4y = -13.